Orlando Mihich and students
The word tessellation comes to us from the Latin tessella, which was the small, square stone or tile used in ancient Roman mosaics. Tessellations are thousands of years old and can be found all over the world in a variety of cultures and in a variety of forms. They can be traced all the way back to the Sumerian civilization (about 4000 B.C.) in which the walls of homes and temples were decorated by designs of tessellations constructed from slabs of hardened clay. Not only did these tessellations provide decoration but they also became part of the structure of the buildings. Since then, tessellations have been found in many of the artistic elements of wide-ranging cultures including the Egyptians, Moors, Romans, Persians, Greek, Byzantine, Arabic, Japanese, and Chinese.
The kinds of shapes used in the tilings vary between culture to culture. Coloring techniques, which can make tremendous differences in the overall visual effect of a tessellation, also vary from culture to culture. Finally, the amount of embellishment added to the tilings varies among the artwork in each culture.
For example, the Islamic religion forbids
the representation of living objects in works of art. The Moors have
consequently created only abstract geometrical works composed of
simple shapes. Nevertheless, their works of intricate design are
nothing short of breathtaking. On the other hand, Romans and other
Mediterranean peoples have incorporated detailed illustrations of
humans and natural scenes into their designs.
Probably the best known example of
tessellated patterns has been the Alhambra palace, an Islamic
architectural marvel located in Granada, Spain. Its floors, walls,
and ceilings are literally covered with tessellations and other
repeating patterns.
In recent times, tessellations have appeared on floors, walls,
ceilings, and buildings, and in ceramics, clothing designs, rugs,
wallpaper, and stained-glass windows. They have continued to be an
art form with artists such as Maurits Escher, Victor Vasarely, and
Bridget Riley, who have explored variations and extensions of tilings
on the plane.
Logo (MicroWorlds) is a language for learning, it is derived from LISP, the language of artificial intelligence. Logo involves the student beyond moving the turtle or using mathematics. Logo involves thinking about processes, about how you are doing what you are doing. "From an educational point of view, Logo represents a window into the mind. Looking at students' programs we have ways of understanding how their minds worked in the process of developing the programs, and the level of knowledge, strategies, and style used" (Valente, 1995). Programming allows the computer user to have better control over the computer. The reason Papert prefers programming over ready-made educational software is that "discovery cannot be a setup and invention cannot be scheduled." (Papert, 1980).
Following are examples of tessellations done with Logo by seventh grade Delta students at MS 54 in New York City during the 1998-1999 school year.
